Conditions for unique graph realizations
SIAM Journal on Computing
Planar minimally rigid graphs and pseudo-triangulations
Proceedings of the nineteenth annual symposium on Computational geometry
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Connected rigidity matroids and unique realizations of graphs
Journal of Combinatorial Theory Series B
On constructive characterizations of (k,l)-sparse graphs
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Combinatorial synthesis approach employing graph networks
Advanced Engineering Informatics
Connectivity-based localization of large-scale sensor networks with complex shape
ACM Transactions on Sensor Networks (TOSN)
Fully Decentralized, Collaborative Multilateration Primitives for Uniquely Localizing WSNs
WASA '09 Proceedings of the 4th International Conference on Wireless Algorithms, Systems, and Applications
Rigid tensegrity labelings of graphs
European Journal of Combinatorics
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Globally rigid circuits of the direction--length rigidity matroid
Journal of Combinatorial Theory Series B
Fully decentralized and collaborative multilateration primitives for uniquely localizing WSNs
EURASIP Journal on Wireless Communications and Networking - Special issue on wireless network algorithms, systems, and applications
Combinatorial characterization of the Assur graphs from engineering
European Journal of Combinatorics
Rigidity, global rigidity, and graph decomposition
European Journal of Combinatorics
Beyond triangle inequality: sifting noisy and outlier distance measurements for localization
INFOCOM'10 Proceedings of the 29th conference on Information communications
Beyond triangle inequality: Sifting noisy and outlier distance measurements for localization
ACM Transactions on Sensor Networks (TOSN)
Generic global rigidity of body-bar frameworks
Journal of Combinatorial Theory Series B
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A graph G = (V , E) is called a generic circuit if |E| = 2|V| - 2 and every X ⊂ V with 2 ≥ |X| ≥ |V| - 1 satisfies i(X) ≤ 2|X| - 3. Here i(X) denotes the number of edges induced by X. The operation extension subdivides an edge uw of a graph by a new vertex v and adds a new edge vz for some vertex z ≠ u, w. Connelly conjectured that every 3-connected generic circuit can be obtained from K4 by a sequence of extensions. We prove this conjecture. As a corollary, we also obtain a special case of a conjecture of Hendrickson on generically globally rigid graphs.